Question

Using a 685 nm wavelength laser, you form the diffraction pattern of a 0.119 mm wide slit on a screen. You measure on the screen that the 11th dark fringe is 9.47 cm away from the center of the central maximum. How far is the screen located from the slit?

Answer 1

Destructive interference produces the dark fringes. Dark fringes in the diffraction pattern of a single slit are found at angles θ for which

w sinθ = mλ,

where m is an integer, m = 1, 2, 3, ... .   For the first dark fringe we have w sinθ = λ.

If the interference pattern is viewed on a screen a distance L from the slits, then the wavelength can be found from the spacing of the fringes. We have λ = w sinθ/m and sinθ = z/(L² + z²)^½), or

λ = zw/(m(L² + z²)^½)

L =(( zw/λm)² -z²)^1/2 ————(2)

where z is the distance from the center of the interference pattern to the mth dark line in the pattern

w = width of the slit

L = distance between slit and screen

m = m_th dark fringe

λ = wavelength

Here given, λ= 685 nm = 685* 10^-9 m

m = 11

w = 0.119 mm= 0.119 * 10^-3 m

z = 9.47 cm = 9.47 * 10^-2 m

L = to find??

using above formula,

L = ((9.47 * 10^-2 * 0.119 * 10^-3 / 11 * 685 * 10^-9)² - (9.47 * 10^-2)²)^1/2

= 1.49 m [Answer]